Damped multichannel singular spectrum analysis for 3D random noise attenuation

Huang, Weilin; Wang, Runqiu; Chen, Yangkang; Li, Huijian; Gan, Shuwei

doi:10.1190/geo2015-0264.1

Cited by 254 publications

(34 citation statements)

References 26 publications

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“…In general, R is much less than the size of S w and thus is low rank (LR). Based on this observation, the LR approximation for seismic denoising (Oropeza and Sacchi 2011;Huang et al 2016) first maps the noisy signal into a Hankel matrix, then computes the rank-R approximation of the Hankel matrix, finally obtains the denoised signal by transforming the LR matrix back to the signal domain. However, for real seismic data, there are two important issues that need to be addressed for this approach.…”

Section: O P T I M a L R A N K S E L E C T I O N F O R L O W -R A N Kmentioning

confidence: 99%

“…The damping factor k in (17) is selected according to the noise level and is usually chosen between 2 and 5 Huang et al (2016). Another approach is to use the optimal singular value shrinkage proposed by Nadakuditi (2014):…”

Section: Singular Value Shrinkagementioning

confidence: 99%

“…, σ R (D) are also corrupted by noise. To mitigate this issue, Huang et al (2016) proposed to shrink the singular values by…”

Section: Singular Value Shrinkagementioning

confidence: 99%

“…r We incorporate this rank selection strategy into the classical LR approximation, damped LR approximation (Huang et al 2016) and other methods based on singular value shrinkage. Our second contribution is to establish connection between damped LR approximation and the optimal singular value shrinkage (Nadakuditi 2014), which is statistically optimal when the noise matrix is a Gaussian random matrix.…”

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confidence: 99%

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Low‐rank seismic denoising with optimal rank selection for hankel matrices

Wang

Zhu

2019

Geophysical Prospecting

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A B S T R A C TBased on the fact that the Hankel matrix representing clean seismic data is low rank, low-rank approximation methods have been widely utilized for removing noise from seismic data. A common strategy for real seismic data is to perform the low-rank approximations for small local windows where the events can be approximately viewed as linear. This raises a fundamental question of selecting an optimal rank that best captures the number of events for each local window. Gavish and Donoho proposed a method to select the rank when the noise is independent and identically distributed. Gaussian matrix by analysing the statistical performance of the singular values of the Gaussian matrices. However, such statistical performance is not available for noisy Hankel matrices. In this paper, we adopt the same strategy and propose a rule that computes the number of singular values exceed the median singular value by a multiplicative factor. We suggest a multiplicative factor of 3 based on simulations which mimic the theories underlying Gavish and Donoho in the independent and identically distributed Gaussian setting. The proposed optimal rank selection rule can be incorporated into the classical low-rank approximation method and many other recently developed methods such as those by shrinking the singular values. The low-rank approximation methods with optimally selected rank rule can automatically suppress most of the noise while preserving the main features of the seismic data in each window. Experiments on both synthetic and field seismic data demonstrate the superior performance of the proposed rank selection rule for seismic data denoising.

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Section: O P T I M a L R A N K S E L E C T I O N F O R L O W -R A N Kmentioning

confidence: 99%

Section: Singular Value Shrinkagementioning

confidence: 99%

“…, σ R (D) are also corrupted by noise. To mitigate this issue, Huang et al (2016) proposed to shrink the singular values by…”

Section: Singular Value Shrinkagementioning

confidence: 99%

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confidence: 99%

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Low‐rank seismic denoising with optimal rank selection for hankel matrices

Wang

Zhu

2019

Geophysical Prospecting

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“…Naghizadeh and Sacchi (2013) address the problem of interpolation beyond aliasing in the Cadzow reconstruction. Huang et al (2016) indicate that SVD actually decomposes the data into a noise subspace and a signal-plus-noise subspace, and derive a new formula of rank-reduction, named damped SVD, which can theoretically remove the noise from the signal-plus-noise subspace. Chen et al (2016b) further extend this damped algorithm to five-dimensional seismic data reconstruction in the presence of random noise, where the damped SVD is applied to the level-4 block Hankel matrix.…”

Section: Introductionmentioning

confidence: 99%

De‐aliased and de‐noise Cadzow filtering for seismic data reconstruction

Huang

Feng

Chen

2019

Geophysical Prospecting

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Cadzow filtering is currently considered as one of the most effective approaches for seismic data reconstruction. The basic version of Cadzow filtering first reorders each frequency slice of the seismic data (to be reconstructed) to a block Hankel/Toeplitz matrix, and then implements a rank‐reduction operator, that is truncated singular value decomposition, to the Hankel/Toeplitz matrix. However, basic Cadzow filtering cannot deal with the problem of recovering regularly missing data (up‐sampling) in the case of strongly aliased energy, because the regularly missing data will mix with signals in the singular spectrum. To solve this problem, it has been proposed to precondition the reconstruction of high‐frequency components using information from the low‐frequency components which are less aliased. In this paper, we further extend the de‐aliased Cadzow filtering approach to reconstruct regularly sampled seismic traces from the noisy observed data by modifying the reinserting operation, in which the high‐frequency components are projected onto the sub‐space spanned by several singular vectors of the low‐frequency components. At each iteration, the filtered data are weighted to the original data as a feedback. The weighting factor is related to the background noise level and changes with iteration. The feasibility of the proposed technique is validated via two‐dimensional, three‐dimensional and five‐dimensional synthetic data examples, as well as two‐dimensional post‐stack and three‐dimensional pre‐stack field data examples. The results demonstrate that the proposed technique can effectively interpolate regularly sampled data and is robust in noisy environments.

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